The consistent element nodal loads vector re given by the Eq. (21) converts loads distributed throughout an element or over its surface or from initial strains or stress to discrete loads at element nodes. These loads are called consistent because they are based on the same shape functions as used to calculate the element stiffness matrix. Moreover these loads are statically equivalent to the original distributed loading; both re and the original loading have the same resultant force and the same moment about an arbitrarily chosen point.
These loads are called work equivalent loads for the following reason: work done by nodal loads re in going through nodal displacements d is equal to work done by distributed loads F and Φ in going through the displacement field associated with element shape function:
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(60) |
The later integral sums the work of force increments ΦdS in going through displacements u where u are field displacements created by d via shape functions N.
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